> ## Documentation Index
> Fetch the complete documentation index at: https://aitutorial.dev/llms.txt
> Use this file to discover all available pages before exploring further.

# How Images Become Tensors

> Representing images, videos, and volumetric studies as matrices and tensors

export const QuizQuestion = ({question, options, answer, explanation}) => {
  const [selected, setSelected] = useState(null);
  const [revealed, setRevealed] = useState(false);
  const handleSelect = index => {
    if (revealed) return;
    setSelected(index);
    setRevealed(true);
  };
  const isCorrect = selected === answer;
  const getOptionClass = i => {
    const classes = ['quiz-option'];
    if (revealed) {
      classes.push('quiz-option-disabled');
      if (i === answer) classes.push('quiz-option-correct'); else if (i === selected && !isCorrect) classes.push('quiz-option-wrong');
    }
    return classes.join(' ');
  };
  return <div className="quiz-card">
      <p className="quiz-question">{question}</p>
      <div className="quiz-options">
        {options.map((option, i) => <button key={i} onClick={() => handleSelect(i)} className={getOptionClass(i)}>
            <span className="quiz-letter">{String.fromCharCode(65 + i)}</span>
            {option}
          </button>)}
      </div>
      {revealed && <div className={`quiz-feedback ${isCorrect ? 'quiz-feedback-correct' : 'quiz-feedback-wrong'}`}>
          <strong>{isCorrect ? 'Correct!' : 'Incorrect.'}</strong> {explanation}
        </div>}
    </div>;
};

export const Quiz = ({title = "Check Your Understanding", children}) => {
  return <div style={{
    marginTop: '24px'
  }}>
      <div className="quiz-title">{title}</div>
      {children}
    </div>;
};

export const CodeEditor = ({file = 'src/hello_world.ts', lines, title = 'Code Example', repo = 'ai-tutorial/typescript-examples', height = '650px', functionName, theme: userTheme}) => {
  const STORAGE_KEY = 'openai_api_key';
  const GEMINI_STORAGE_KEY = 'gemini_api_key';
  const ANTHROPIC_STORAGE_KEY = 'anthropic_api_key';
  const PROVIDER_STORAGE_KEY = 'llm_playground_provider';
  if (!functionName) {
    console.warn('CodeEditor: functionName parameter is required');
  }
  const hasCreatedEnvRef = useRef(false);
  const vmRef = useRef(null);
  const [isMaximized, setIsMaximized] = useState(false);
  const [isCollapsed, setIsCollapsed] = useState(false);
  const [isStuck, setIsStuck] = useState(false);
  const [iframeKey, setIframeKey] = useState(0);
  const [showApiKeyDialog, setShowApiKeyDialog] = useState(false);
  const [apiKey, setApiKey] = useState('');
  const [error, setError] = useState('');
  const [success, setSuccess] = useState(false);
  const [isSubmitting, setIsSubmitting] = useState(false);
  const [isValidating, setIsValidating] = useState(false);
  const [detectedTheme, setDetectedTheme] = useState('dark');
  useEffect(() => {
    if (typeof window === 'undefined') return;
    const checkTheme = () => {
      const isDark = document.documentElement.classList.contains('dark');
      setDetectedTheme(isDark ? 'dark' : 'light');
    };
    checkTheme();
    const observer = new MutationObserver(checkTheme);
    observer.observe(document.documentElement, {
      attributes: true,
      attributeFilter: ['class']
    });
    return () => observer.disconnect();
  }, []);
  const theme = userTheme || detectedTheme;
  const [selectedProvider, setSelectedProvider] = useState(() => {
    if (typeof window === 'undefined') return 'gemini';
    return localStorage.getItem(PROVIDER_STORAGE_KEY) || 'gemini';
  });
  const isApiKeyConfigured = () => {
    const openaiKey = localStorage.getItem(STORAGE_KEY);
    const geminiKey = localStorage.getItem(GEMINI_STORAGE_KEY);
    const anthropicKey = localStorage.getItem(ANTHROPIC_STORAGE_KEY);
    return openaiKey !== null && openaiKey.trim().length > 0 || geminiKey !== null && geminiKey.trim().length > 0 || anthropicKey !== null && anthropicKey.trim().length > 0;
  };
  const dispatchApiKeyChanged = () => {
    if (typeof window !== 'undefined' && window.dispatchEvent) {
      window.dispatchEvent(new CustomEvent('apiKeyChanged', {
        detail: {
          configured: isApiKeyConfigured()
        }
      }));
    }
  };
  const saveApiKey = apiKey => {
    if (apiKey && apiKey.trim()) {
      const trimmedKey = apiKey.trim();
      localStorage.setItem(STORAGE_KEY, trimmedKey);
      dispatchApiKeyChanged();
      return true;
    }
    return false;
  };
  const buildEnvContent = () => {
    const openaiKey = localStorage.getItem(STORAGE_KEY)?.trim();
    const geminiKey = localStorage.getItem(GEMINI_STORAGE_KEY)?.trim();
    const anthropicKey = localStorage.getItem(ANTHROPIC_STORAGE_KEY)?.trim();
    if (!openaiKey && !geminiKey && !anthropicKey) {
      return `OPENAI_MODEL=gpt-4.1-nano
OPENAI_API_KEY=sk-mock-key-1234567890abcdef
GEMINI_MODEL=gemini-2.5-flash-lite
GOOGLE_GENERATIVE_AI_API_KEY=
GOOGLE_API_KEY=
ANTHROPIC_API_KEY=
AI_PROVIDER=openai
# API key not found in browser storage
# To configure your API key:
# 1. For Gemini (free): Go to https://aistudio.google.com/apikey
# 2. For OpenAI: Go to https://platform.openai.com/api-keys
# 3. For Claude: Go to https://console.anthropic.com/settings/keys
# 4. Enter it in the configuration form above this editor
# 5. The .env file will be automatically updated with your key`;
    }
    const envLines = ['# Using the API key(s) you configured. This file will be created when the dialog is loaded.'];
    if (openaiKey) {
      envLines.push(`OPENAI_MODEL=gpt-4.1-nano`);
      envLines.push(`OPENAI_API_KEY=${openaiKey}`);
    }
    if (geminiKey) {
      envLines.push(`GEMINI_MODEL=gemini-2.5-flash-lite`);
      envLines.push(`# Vercel AI SDK uses GOOGLE_GENERATIVE_AI_API_KEY, LangChain uses GOOGLE_API_KEY`);
      envLines.push(`GOOGLE_GENERATIVE_AI_API_KEY=${geminiKey}`);
      envLines.push(`GOOGLE_API_KEY=${geminiKey}`);
    }
    if (anthropicKey) {
      envLines.push(`ANTHROPIC_API_KEY=${anthropicKey}`);
    }
    const provider = anthropicKey ? 'anthropic' : geminiKey ? 'gemini' : 'openai';
    envLines.push(`AI_PROVIDER=${provider}`);
    return envLines.join('\n');
  };
  const updateEnvFile = async vm => {
    if (!vm) return;
    try {
      await vm.applyFsDiff({
        create: {
          'env/.env': buildEnvContent(),
          'env/run.conf': `file=${file}`
        },
        destroy: []
      });
      hasCreatedEnvRef.current = true;
    } catch (error) {
      console.error('Failed to write env files:', error);
      hasCreatedEnvRef.current = false;
    }
  };
  useEffect(() => {
    if (!isApiKeyConfigured()) {
      setShowApiKeyDialog(true);
    }
    const handleApiKeyChanged = () => {
      if (isApiKeyConfigured()) {
        setShowApiKeyDialog(false);
      }
    };
    if (typeof window !== 'undefined') {
      window.addEventListener('apiKeyChanged', handleApiKeyChanged);
      return () => {
        window.removeEventListener('apiKeyChanged', handleApiKeyChanged);
      };
    }
  }, []);
  const validateApiKey = async (key, provider) => {
    try {
      const urls = {
        gemini: 'https://generativelanguage.googleapis.com/v1beta/models?key=' + encodeURIComponent(key.trim()),
        openai: 'https://api.openai.com/v1/models',
        anthropic: 'https://api.anthropic.com/v1/models'
      };
      const headerMap = {
        gemini: {
          'Content-Type': 'application/json'
        },
        openai: {
          'Authorization': `Bearer ${key.trim()}`,
          'Content-Type': 'application/json'
        },
        anthropic: {
          'x-api-key': key.trim(),
          'anthropic-version': '2023-06-01',
          'Content-Type': 'application/json'
        }
      };
      const url = urls[provider];
      const headers = headerMap[provider];
      const response = await fetch(url, {
        method: 'GET',
        headers
      });
      if (response.ok) {
        return {
          valid: true
        };
      } else if (response.status === 401 || response.status === 403) {
        return {
          valid: false,
          error: 'Invalid API key. Please check your key and try again.'
        };
      } else if (response.status === 429) {
        return {
          valid: false,
          error: 'Rate limit exceeded. Please try again later.'
        };
      } else {
        const errorData = await response.json().catch(() => ({}));
        return {
          valid: false,
          error: errorData.error?.message || `API request failed with status ${response.status}`
        };
      }
    } catch (err) {
      if (err.name === 'TypeError' && err.message.includes('fetch')) {
        return {
          valid: false,
          error: 'Network error. Please check your connection and try again.'
        };
      }
      return {
        valid: false,
        error: err.message || 'Failed to validate API key. Please try again.'
      };
    }
  };
  const handleSkipConfiguration = () => {
    const skipKey = 'sk-<configure-your-key>';
    saveApiKey(skipKey);
    setShowApiKeyDialog(false);
  };
  const handleApiKeySubmit = async e => {
    e.preventDefault();
    setError('');
    setSuccess(false);
    setIsSubmitting(true);
    const providerNames = {
      gemini: 'Gemini',
      openai: 'OpenAI',
      anthropic: 'Claude'
    };
    if (!apiKey || !apiKey.trim()) {
      setError(`Please enter your ${providerNames[selectedProvider]} API key`);
      setIsSubmitting(false);
      return;
    }
    const trimmedKey = apiKey.trim();
    if (selectedProvider === 'openai' && !trimmedKey.startsWith('sk-')) {
      setError('Invalid API key format. OpenAI API keys should start with "sk-"');
      setIsSubmitting(false);
      return;
    }
    if (selectedProvider === 'anthropic' && !trimmedKey.startsWith('sk-ant-')) {
      setError('Invalid API key format. Anthropic API keys should start with "sk-ant-"');
      setIsSubmitting(false);
      return;
    }
    setIsValidating(true);
    setError('');
    const validation = await validateApiKey(trimmedKey, selectedProvider);
    setIsValidating(false);
    if (!validation.valid) {
      setError(validation.error || 'Invalid API key. Please check your key and try again.');
      setIsSubmitting(false);
      return;
    }
    try {
      const storageKeys = {
        gemini: GEMINI_STORAGE_KEY,
        openai: STORAGE_KEY,
        anthropic: ANTHROPIC_STORAGE_KEY
      };
      localStorage.setItem(storageKeys[selectedProvider], trimmedKey);
      localStorage.setItem(PROVIDER_STORAGE_KEY, selectedProvider);
      dispatchApiKeyChanged();
      setSuccess(true);
      setApiKey('');
      setTimeout(() => {
        window.location.reload();
      }, 1000);
    } catch (err) {
      setError(err.message || 'Failed to save API key. Please try again.');
      setIsSubmitting(false);
    }
  };
  const baseFilePath = file || 'src/hello_world.ts';
  let filePath = baseFilePath;
  if (typeof lines === 'string' && lines.trim()) {
    const lineParts = lines.split('-');
    if (lineParts.length === 2) {
      filePath = `${filePath}:L${lineParts[0].trim()}-L${lineParts[1].trim()}`;
    } else {
      filePath = `${filePath}:L${lineParts[0].trim()}`;
    }
  } else if (typeof lines === 'object' && lines.start !== undefined) {
    filePath = lines.end !== undefined ? `${filePath}:L${lines.start}-L${lines.end}` : `${filePath}:L${lines.start}`;
  }
  const stackblitzUrl = `https://stackblitz.com/github/${repo}?file=${encodeURIComponent(filePath)}&embed=1&view=editor&theme=${theme}`;
  const loadSDK = () => {
    return new Promise((resolve, reject) => {
      if (window.StackBlitzSDK || window.stackblitzSDK) {
        resolve(window.StackBlitzSDK || window.stackblitzSDK);
        return;
      }
      if (document.querySelector('script[data-stackblitz-sdk]')) {
        const checkInterval = setInterval(() => {
          if (window.StackBlitzSDK || window.stackblitzSDK) {
            clearInterval(checkInterval);
            resolve(window.StackBlitzSDK || window.stackblitzSDK);
          }
        }, 100);
        setTimeout(() => {
          clearInterval(checkInterval);
          reject(new Error('SDK loading timeout'));
        }, 10000);
        return;
      }
      const script = document.createElement('script');
      script.src = 'https://unpkg.com/@stackblitz/sdk/bundles/sdk.umd.js';
      script.async = true;
      script.setAttribute('data-stackblitz-sdk', 'true');
      script.onload = () => {
        const sdk = window.StackBlitzSDK || window.stackblitzSDK;
        if (sdk) {
          resolve(sdk);
        } else {
          reject(new Error('SDK loaded but not available on window'));
        }
      };
      script.onerror = () => {
        reject(new Error('Failed to load StackBlitz SDK'));
      };
      document.head.appendChild(script);
    });
  };
  const LOAD_TIMEOUT_MS = 10000;
  const iframeElRef = useRef(null);
  const reloadCountRef = useRef(0);
  const handleRetry = () => {
    vmRef.current = null;
    hasCreatedEnvRef.current = false;
    reloadCountRef.current = 0;
    setIsStuck(false);
    setIframeKey(prev => prev + 1);
  };
  const iframeRef = iframe => {
    iframeElRef.current = iframe;
  };
  const connectToVM = async iframe => {
    const sdk = await loadSDK();
    return sdk.connect(iframe);
  };
  const handleIframeLoad = async () => {
    const iframe = iframeElRef.current;
    if (!iframe) return;
    if (reloadCountRef.current > 0) {
      try {
        const vm = await connectToVM(iframe);
        vmRef.current = vm;
        await updateEnvFile(vm);
      } catch (_) {}
      return;
    }
    try {
      if (vmRef.current) return;
      const vm = await Promise.race([connectToVM(iframe), new Promise((_, reject) => setTimeout(() => reject(new Error('connect timeout')), LOAD_TIMEOUT_MS))]);
      vmRef.current = vm;
      await updateEnvFile(vm);
    } catch (error) {
      console.error('Failed to connect to StackBlitz VM:', error);
      if (typeof window !== 'undefined' && window.gtag) {
        window.gtag('event', 'load_refresh_error', {
          event_category: 'stackblitz',
          event_label: file,
          error_message: error.message
        });
      }
      reloadCountRef.current = 1;
      setTimeout(() => {
        setIframeKey(prev => prev + 1);
      }, 2000);
    }
  };
  const isSafari = typeof navigator !== 'undefined' && (/^((?!chrome|android).)*safari/i).test(navigator.userAgent);
  if (isSafari) {
    return <div className="code-editor-dialog-container" style={{
      height: height
    }}>
        <div className="code-editor-dialog-box">
          <h2 className="code-editor-dialog-title">
            <svg width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="#f59e0b" strokeWidth="2">
              <path d="M10.29 3.86L1.82 18a2 2 0 0 0 1.71 3h16.94a2 2 0 0 0 1.71-3L13.71 3.86a2 2 0 0 0-3.42 0z"></path>
              <line x1="12" y1="9" x2="12" y2="13"></line>
              <line x1="12" y1="17" x2="12.01" y2="17"></line>
            </svg>
            Browser Not Supported
          </h2>
          <p className="code-editor-dialog-description">
            The interactive code editor is not supported on Safari. Please use <strong>Chrome</strong>, <strong>Edge</strong>, or <strong>Firefox</strong> to run the examples.
          </p>
        </div>
      </div>;
  }
  if (showApiKeyDialog) {
    return <div className="code-editor-dialog-container" style={{
      height: height
    }}>
        <div className="code-editor-dialog-box">
          <h2 className="code-editor-dialog-title">
            <svg width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="#f59e0b" strokeWidth="2">
              <path d="M10.29 3.86L1.82 18a2 2 0 0 0 1.71 3h16.94a2 2 0 0 0 1.71-3L13.71 3.86a2 2 0 0 0-3.42 0z"></path>
              <line x1="12" y1="9" x2="12" y2="13"></line>
              <line x1="12" y1="17" x2="12.01" y2="17"></line>
            </svg>
            Configure API Key
          </h2>

          <p className="code-editor-dialog-description">
            All interactive examples execute entirely within your browser environment, ensuring complete security and privacy.
            Your API key is stored locally in your browser's storage and is never transmitted to external servers.
          </p>

          <div className="llm-provider-tabs" style={{
      marginBottom: '16px'
    }}>
            <button type="button" onClick={() => {
      setSelectedProvider('gemini');
      setError('');
      setApiKey('');
    }} className={`llm-provider-tab ${selectedProvider === 'gemini' ? 'llm-provider-tab-active' : ''}`}>
              Gemini <span className="llm-provider-tab-badge">Free</span>
            </button>
            <button type="button" onClick={() => {
      setSelectedProvider('openai');
      setError('');
      setApiKey('');
    }} className={`llm-provider-tab ${selectedProvider === 'openai' ? 'llm-provider-tab-active' : ''}`}>
              OpenAI
            </button>
            <button type="button" onClick={() => {
      setSelectedProvider('anthropic');
      setError('');
      setApiKey('');
    }} className={`llm-provider-tab ${selectedProvider === 'anthropic' ? 'llm-provider-tab-active' : ''}`}>
              Claude
            </button>
          </div>

          {selectedProvider === 'gemini' && <div className="llm-gemini-recommendation" style={{
      marginBottom: '16px'
    }}>
              Gemini offers a generous free tier — great for learning! Get your free API key at{' '}
              <a href="https://aistudio.google.com/apikey" target="_blank" rel="noopener noreferrer" className="code-editor-link">
                aistudio.google.com/apikey
              </a>
            </div>}

          {selectedProvider === 'openai' && <div className="code-editor-info-box">
              <p className="code-editor-info-box-title">
                Don't have an API key?
              </p>
              <p className="code-editor-info-box-text">
                Get one at{' '}
                <a href="https://platform.openai.com/api-keys" target="_blank" rel="noopener noreferrer" className="code-editor-link">
                  platform.openai.com/api-keys
                </a>
              </p>
            </div>}

          {selectedProvider === 'anthropic' && <div className="code-editor-info-box">
              <p className="code-editor-info-box-title">
                Don't have an API key?
              </p>
              <p className="code-editor-info-box-text">
                Get one at{' '}
                <a href="https://console.anthropic.com/settings/keys" target="_blank" rel="noopener noreferrer" className="code-editor-link">
                  console.anthropic.com/settings/keys
                </a>
              </p>
            </div>}

          <form onSubmit={handleApiKeySubmit}>
            <div className="code-editor-form-group">
              <label htmlFor="api-key-input" className="code-editor-label">
                {selectedProvider === 'gemini' ? 'Gemini' : 'OpenAI'} API Key
              </label>
              <input id="api-key-input" type="password" value={apiKey} onChange={e => {
      setApiKey(e.target.value);
      setError('');
      setSuccess(false);
    }} placeholder={selectedProvider === 'openai' ? 'sk-...' : 'Gemini API Key'} disabled={isSubmitting} className={`code-editor-input ${error ? 'code-editor-input-error' : ''}`} />
            </div>

            {isValidating && <div className="code-editor-message code-editor-message-info">
                <span className="code-editor-message-icon">⏳</span>
                <span>Validating API key...</span>
              </div>}

            {error && !isValidating && <div className="code-editor-message code-editor-message-error">
                <span className="code-editor-message-icon">⚠️</span>
                <span>{error}</span>
              </div>}

            {success && <div className="code-editor-message code-editor-message-success">
                <span className="code-editor-message-icon">✓</span>
                <span>API key saved successfully! Loading editor...</span>
              </div>}

            <button type="submit" disabled={isSubmitting || isValidating || !apiKey.trim()} className="code-editor-button">
              {isValidating ? 'Validating...' : isSubmitting ? 'Saving...' : 'Save API Key'}
            </button>
          </form>

          <button type="button" onClick={handleSkipConfiguration} disabled={isSubmitting || isValidating} className="code-editor-button-secondary">
            Skip Configuration
          </button>

          <div className="code-editor-footer">
            <p className="code-editor-footer-text">
              Alternatively, you may checkout the source code from{' '}
              <a href="https://github.com/ai-tutorial/typescript-examples" target="_blank" rel="noopener noreferrer" className="code-editor-link code-editor-link-break">
                https://github.com/ai-tutorial/typescript-examples
              </a>
              {' '}and run the examples locally.
            </p>
          </div>
        </div>
      </div>;
  }
  const toggleMaximize = () => setIsMaximized(!isMaximized);
  const toggleCollapse = () => setIsCollapsed(!isCollapsed);
  return <div className={`code-editor-wrapper ${isMaximized ? 'maximized' : ''} ${isCollapsed ? 'collapsed' : ''}`} data-theme={theme}>
      <div className="code-editor-header">
        <div className="code-editor-title">
          <svg width="14" height="14" viewBox="0 0 24 24" fill="none" stroke="currentColor" strokeWidth="2" strokeLinecap="round" strokeLinejoin="round">
            <path d="M11 4H4a2 2 0 0 0-2 2v14a2 2 0 0 0 2 2h14a2 2 0 0 0 2-2v-7"></path>
            <path d="M18.5 2.5a2.121 2.121 0 0 1 3 3L12 15l-4 1 1-4 9.5-9.5z"></path>
          </svg>
          {title}
        </div>
        <div className="code-editor-controls">
          {!isMaximized && <button className="code-editor-collapse-button" onClick={toggleCollapse} title={isCollapsed ? "Expand" : "Collapse"} type="button">
              <svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" strokeWidth="2" strokeLinecap="round" strokeLinejoin="round">
                {isCollapsed ? <polyline points="6 9 12 15 18 9" /> : <polyline points="6 15 12 9 18 15" />}
              </svg>
            </button>}
          <button className="code-editor-maximize-button" onClick={toggleMaximize} title={isMaximized ? "Minimize" : "Maximize (Focus Mode)"} type="button">
            <svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" strokeWidth="2" strokeLinecap="round" strokeLinejoin="round">
              {isMaximized ? <><path d="M4 14h6v6" /><path d="M20 10h-6V4" /><path d="M14 10l7-7" /><path d="M3 21l7-7" /></> : <><path d="M15 3h6v6" /><path d="M9 21H3v-6" /><path d="M21 3l-7 7" /><path d="M3 21l7-7" /></>}
            </svg>
          </button>
        </div>
      </div>

      {!isCollapsed && <div style={{
    position: 'relative',
    height: isMaximized ? 'auto' : height,
    flex: isMaximized ? 1 : 'none'
  }}>
          <iframe key={iframeKey} ref={iframeRef} onLoad={handleIframeLoad} src={stackblitzUrl} className="code-editor-iframe" style={{
    height: '100%',
    flex: isMaximized ? 1 : 'none'
  }} title={title || 'Code Example'} allow="accelerometer; camera; encrypted-media; geolocation; gyroscope; hid; microphone; midi; payment; usb; xr-spatial-tracking" sandbox="allow-forms allow-modals allow-popups allow-presentation allow-same-origin allow-scripts" />

          {isStuck && <div className="code-editor-stuck-overlay">
              <div className="code-editor-stuck-box">
                <svg width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="#f59e0b" strokeWidth="2">
                  <path d="M10.29 3.86L1.82 18a2 2 0 0 0 1.71 3h16.94a2 2 0 0 0 1.71-3L13.71 3.86a2 2 0 0 0-3.42 0z"></path>
                  <line x1="12" y1="9" x2="12" y2="13"></line>
                  <line x1="12" y1="17" x2="12.01" y2="17"></line>
                </svg>
                <p>StackBlitz is taking too long to load. This can happen when the repository was recently updated.</p>
                <button type="button" className="code-editor-button" onClick={handleRetry} style={{
    marginTop: '8px'
  }}>
                  Retry
                </button>
              </div>
            </div>}
        </div>}
    </div>;
};

Before any model, every vision pipeline does the same thing: it reads pixels off disk and turns them into a tensor with a specific shape. Get the shape wrong and nothing downstream works. This page covers the mental model for images, videos, and volumetric studies, and the tensor layouts you will see over and over again.

## Pixels Are Just Numbers

A grayscale image is a grid of brightness values. A 28×28 MNIST digit is literally a 2D matrix of 784 numbers, each between 0 and 255 (or scaled to `[0, 1]` before feeding a network):

```text theme={null}
Grayscale image → shape: (H, W)

         col 0  col 1  col 2  ...  col 27
 row  0 [  0      0    120   ...    0   ]
 row  1 [  0    230    255   ...    0   ]
  ...
 row 27 [  0      0      0   ...    0   ]
```

A color image adds a third axis for channels. Each pixel stores three intensities (Red, Green, Blue), so a 224×224 RGB image is a tensor of shape `(H, W, 3)` — or `(3, H, W)` depending on framework convention. Remember this because it is the single most common source of "my tensor has the wrong shape" errors.

| Framework                                   | Preferred layout | Mnemonic         |
| ------------------------------------------- | ---------------- | ---------------- |
| PyTorch, Caffe, many vision libs            | `(C, H, W)`      | "channels first" |
| TensorFlow / Keras, NumPy image I/O, Pillow | `(H, W, C)`      | "channels last"  |

**Batches** stack multiple images along a new leading axis:

```text theme={null}
Batch of RGB images → (N, C, H, W) in PyTorch
                   → (N, H, W, C) in TensorFlow
```

## Videos Add Time

A video is a sequence of frames, so it adds a temporal axis. The most common layout is:

```text theme={null}
Video clip → (T, C, H, W)   or   (N, T, C, H, W) for a batch
```

where `T` is the number of frames. Early video models flattened time into the channel dimension (`3 × T` channels); modern ones treat time explicitly, either with 3D convolutions (`Conv3D`), temporal attention, or by tubeletizing patches like a ViT. The representation is the same three-digit tensor you already know — just one dimension longer.

## Volumetric Studies: CT, MRI, and Friends

Medical imaging is where many newcomers trip, because "a scan" is not a single image. A CT or MRI study is a stack of 2D cross-sections through the body, and each one is a separate grayscale image.

```text theme={null}
CT / MRI volume → (D, H, W)          single-channel volumetric
                (C, D, H, W)         multi-modality (e.g. T1 + T2 + FLAIR for MRI)
                (N, C, D, H, W)      batch of volumes
```

* **D** ("depth" or "slices") is the number of cross-sections, typically 30–500 for CT, 100–300 for MRI per sequence.
* **MRI** is inherently multi-channel: the same anatomy is imaged with different pulse sequences (T1, T2, FLAIR, DWI), each highlighting different tissue properties. You stack them as channels, just like RGB.
* **Spacing matters.** Unlike natural images, medical volumes carry physical units: each voxel is, say, `0.8 × 0.8 × 3.0 mm`. Networks are not scale-aware — if you train on 1mm-spaced scans and run on 3mm-spaced scans, you will silently degrade. Resampling to a canonical spacing is a standard preprocessing step.

Other "not-quite-a-picture" data follows the same pattern:

* **Hyperspectral imagery:** `(H, W, C)` where `C` can be 100+ wavelength bands (satellite remote sensing).
* **Point clouds from LiDAR:** `(N, 3)` or `(N, 4)` for `(x, y, z, intensity)` — not a grid, handled by PointNet-style architectures.
* **Depth maps:** `(H, W)` with floats — distance in meters per pixel.

## The Preprocessing Pipeline

Almost every image you feed a network goes through the same stages:

```text theme={null}
 File on disk (JPEG/PNG/DICOM/NIfTI)
        |
        v
  Decode  → HxW[xC] array of uint8 / int16
        |
        v
  Resize / crop  → match the model's expected input
        |
        v
  Normalize     → divide by 255, subtract mean, divide by std
        |
        v
  Reorder axes  → (C, H, W) for PyTorch, (H, W, C) for TF
        |
        v
  Stack into a batch → (N, C, H, W)
```

Skip any of these, and you get either silent quality degradation (forgotten normalization) or a hard crash (wrong axis order).

## Inspecting Tensors In Practice

The worked example loads a JPEG, a short video clip, and a NIfTI volume and prints their shapes side-by-side so you can feel the difference.

<CodeEditor file="src/computer-vision/tensor_explorer.ts" functionName="main" lines="1-60" title="Tensor shapes for images, video, and volumes (placeholder)" />

### Practical Implication

Many "my model outputs nonsense" bugs come from shape mistakes that the framework happily accepts because the numbers still multiply. Always log `.shape` (and `.dtype`) at the boundaries of your pipeline — after decode, after normalization, right before the forward pass — rather than trusting the documentation of the library you called three lines above.

#### ❌ Antipattern

```python theme={null}
img = load_image("digit.png")
pred = model(img)   # shape surprise: model expected (1, 1, 28, 28), got (28, 28, 1)
```

#### ✅ Best Practice

```python theme={null}
img = load_image("digit.png")
assert img.shape == (28, 28), f"unexpected shape {img.shape}"
img = img[None, None, :, :].astype("float32") / 255.0   # (1, 1, 28, 28)
pred = model(img)
```

<Quiz>
  <QuizQuestion question="You trained an MRI segmentation model on studies resampled to 1×1×1 mm spacing. At inference time you feed it raw scans without resampling and accuracy collapses. Why?" options={["The model overfit the training set", "Convolution kernels operate in voxel units, not millimeters — different physical spacing changes effective receptive field and breaks the learned scale", "MRI volumes should be converted to RGB before inference"]} answer={1} explanation="Networks are not scale-aware. A 3mm-spaced scan makes every anatomical structure span fewer voxels than training time, so a kernel that covered, say, 9mm during training now covers 27mm. Resample to a canonical spacing before any model call." />

  <QuizQuestion question="You load a color image with Pillow (shape `(H, W, 3)`) and pass it directly to a PyTorch model trained with torchvision. It runs but the predictions are garbage. What's the most likely cause?" options={["You forgot to convert to grayscale", "PyTorch expects channels-first `(3, H, W)`; you fed channels-last, so the 'channels' axis is being interpreted as spatial pixels", "The model needs a larger batch size"]} answer={1} explanation="Channels-first vs channels-last is the classic silent failure in vision pipelines. The tensor has the right total size so the framework doesn't complain — but every convolution now sees nonsense." />
</Quiz>